H2, CO2, and CH4 Adsorption Potential of Kerogen as a Function of Pressure, Temperature, and Maturity

We performed molecular dynamics simulation to elucidate the adsorption behavior of hydrogen (H2), carbon dioxide (CO2), and methane (CH4) on four sub-models of type II kerogens (organic matter) of varying thermal maturities over a wide range of pressures (2.75 to 20 MPa) and temperatures (323 to 423 K). The adsorption capacity was directly correlated with pressure but indirectly correlated with temperature, regardless of the kerogen or gas type. The maximum adsorption capacity was 10.6 mmol/g for the CO2, 7.5 mmol/g for CH4, and 3.7 mmol/g for the H2 in overmature kerogen at 20 MPa and 323 K. In all kerogens, adsorption followed the trend CO2 > CH4 > H2 attributed to the larger molecular size of CO2, which increased its affinity toward the kerogen. In addition, the adsorption capacity was directly associated with maturity and carbon content. This behavior can be attributed to a specific functional group, i.e., H, O, N, or S, and an increase in the effective pore volume, as both are correlated with organic matter maturity, which is directly proportional to the adsorption capacity. With the increase in carbon content from 40% to 80%, the adsorption capacity increased from 2.4 to 3.0 mmol/g for H2, 7.7 to 9.5 mmol/g for CO2, and 4.7 to 6.3 mmol/g for CH4 at 15 MPa and 323 K. With the increase in micropores, the porosity increased, and thus II-D offered the maximum adsorption capacity and the minimum II-A kerogen. For example, at a fixed pressure (20 MPa) and temperature (373 K), the CO2 adsorption capacity for type II-A kerogen was 7.3 mmol/g, while type II-D adsorbed 8.9 mmol/g at the same conditions. Kerogen porosity and the respective adsorption capacities of all gases followed the order II-D > II-C > II-B > II-A, suggesting a direct correlation between the adsorption capacity and kerogen porosity. These findings thus serve as a preliminary dataset on the gas adsorption affinity of the organic-rich shale reservoirs and have potential implications for CO2 and H2 storage in organic-rich formations.


Introduction
Global warming is evident and has led to significant adverse impacts on various Earth systems around the globe [1] due to the burning of fossil fuels and the continuous release of greenhouse gases (GHG) [2,3]. In this context, the Paris Agreement was signed by 195 parties to limit global warming to 2 • C in an attempt to maintain it below 1.5 • C by 2050 [4]. Two main strategies for reducing atmospheric concentrations of CO 2 are negative emissions technology and/or switching to low-or zero-carbon fuel sources [5,6]. First, carbon capture and storage (CSS) technology is considered effective negative emission technology that is a necessity, not an option, and can cut 19% of global CO 2 emissions by 2050 [7]. CCS involves capturing CO 2 from stationary sources, e.g., fossil fuel power plants, fuel processing plants, and other industrial plants, particularly iron, steel, cement, and bulk chemical plants. Then, the captured CO 2 is transported through pipelines or ships for storage in underground geological formations, such as saline aquifers, depleted reservoirs, and coal seams [8][9][10][11]. Renewable energy sources are low-or zero-carbon fuel porosity, the maturity indicator, the hydrogen-to-carbon ratio, the oxygen-to-carbon ratio, and the aromatic/aliphatic ratio [63]. Thus, a cross-plot of these features in a classic van Krevelen diagram describes the kerogen of different deposition origins, including type I (lacustrine), type II (marine), type III (terrestrial), and type IV (originating from residues), and the molecular models of these kerogens have been investigated [61].
Out of all kerogen models, type II kerogen is known to be the main origin of unconventional (shale) gas play [52,64]. Type II kerogen is further classified into four categories-immature, top of oil window, middle/end-of-oil window, and overmature-and each model is characterized by its respective maturity indicators [52]. Thus, a few previous studies [52,65,66] have investigated the gas adsorption potential of these four sub-models of type II kerogen. While these investigations have revealed the gas adsorption potential of kerogen, the impact of kerogen maturity on the gas adsorption potential of shales requires further investigation. Moreover, while the area of underground hydrogen storage is advancing, there is still limited research on H 2 storage via adsorption trapping. Only a few studies have reported the H 2 adsorption potential of rocks, e.g., H 2 adsorption on clay [51] and H 2 adsorption in coals [26], and these studies have reported a significant potential for hydrogen adsorption that was sensitive to pressure and temperature. However, the effect of organic matter residing in shale and its maturity has not been evaluated yet for H 2 sorption potential. Moreover, a comparison of H 2 sorption capacity with CO 2 and CH 4 has not been reported, but it is, nevertheless, of great importance in terms of exploring shale as a potential medium for H 2 storage.
This study, therefore, investigated the adsorption behavior of hydrogen (H 2 ), carbon dioxide (CO 2 ), and methane (CH 4 ) on four kerogen (organic matter) samples of varying maturity (A < B < C < D) over a wide regime of pressures (2.75 to 20 MPa) and temperatures (323 to 423 K). The molecular simulations were performed using the grand-canonical Monte Carlo (GCMC) simulation module to mimic subsurface conditions. We also correlated the adsorption capacity of CO 2 , CH 4 , and H 2 to a range of kerogen structural parameters, i.e., atom ratios, % of aromatic carbon, and oxygen atoms. These results provide a fundamental understanding of gas storage in shales and particularly underpin the largescale CO 2 and hydrogen storage potential in organic-rich shale reservoirs and associated decarbonization strategies.

Gases Adsorption Behavior against Pressure
The adsorption of gases (CO 2 , CH 4 , and H 2 ) was investigated for a broad range of pressure regimes (2.75 to 20 MPa) on four kerogen structures (Figure 1a-d). Clearly, gas adsorption on all types of kerogen structures increased with increasing pressure (Figure 1a). Commonly, at a particular pressure and temperature, the adsorption of three gases followed the order CO 2 > CH 4 > H 2 . As an example, for the pressure increment from 2.75 MPa to 20 MPa at 323 K, CO 2 adsorption on II-A kerogen increased nearly 2.2 times (from 3.8 mmol/g to 8.8 mmol/g), 3.4 times (1.6-5.6 mmol/g) in case of CH 4 , and 6.2 times (0.49-3.0 mmol/g) in case of H 2 (Figure 1a). Furthermore, the observed adsorption behavior was likely to plateau beyond pressure 20 MPa. The highest adsorption capacity of CO 2 confirmed its tendency to desorb CH 4 during a coupled enhanced methane recovery and CO 2 sequestration in organic-rich shales, consistent with previous observations [38,50]. When the H 2 adsorption was lowest and thus H 2 could not desorb CH 4   Furthermore, for the immature type II-A kerogen, the highest recorded adsorption capacity was 8.8 mmol/g for CO2 at 323 K and 20 MPa (but less than overmature II-D kerogen). Gas adsorption in II-A kerogen was directly correlated with pressure, which can be attributed to the enhanced van der Waals and electrostatic interactions between the gas molecules (adsorbates) and the surface (adsorbent) at a higher pressure that lead to physisorption.
Similar trends were noted for gas adsorption on II-B (Figure 1b), II-C (Figure 1c), and II-D (Figure 1d), i.e., the increase in adsorption with the increase in pressure. At a lowpressure, the relative adsorption capacities were higher than in the high-pressure range, which can be attributed to the fact that the highest adsorption energy is found in the smallest pores at low pressure at first and then advances toward the larger pores with increased pressure, which in turn decreases the isosteric heat of adsorption [67]. This observation is an indication of pore filling by physisorption in microporous material, as first recom-   Furthermore, for the immature type II-A kerogen, the highest recorded adsorption capacity was 8.8 mmol/g for CO 2 at 323 K and 20 MPa (but less than overmature II-D kerogen). Gas adsorption in II-A kerogen was directly correlated with pressure, which can be attributed to the enhanced van der Waals and electrostatic interactions between the gas molecules (adsorbates) and the surface (adsorbent) at a higher pressure that lead to physisorption.
Similar trends were noted for gas adsorption on II-B (Figure 1b), II-C (Figure 1c), and II-D (Figure 1d), i.e., the increase in adsorption with the increase in pressure. At a low-pressure, the relative adsorption capacities were higher than in the high-pressure range, which can be attributed to the fact that the highest adsorption energy is found in the smallest pores at low pressure at first and then advances toward the larger pores with increased pressure, which in turn decreases the isosteric heat of adsorption [67]. This observation is an indication of pore filling by physisorption in microporous material, as first recommended by Dubinin [68]-a small increase in adsorption with a further increase in pressure until equilibrium is established. As a comparison, in the literature data from Zhao et al. [37] for similar kerogen (without nanopores), the two data points for II-A, II-C, and II-D (at 5 MPa and 323 K and 10 MPa and 323 K, plotted in Figure 1a,c,d) indicated a relatively lower adsorption capacity under similar conditions compared with our results. This underestimation could be attributed to the absence of nanopores with major control over the adsorption behavior, and thus the presence of nanopores (as in our models) suggests greater adsorption capacity.
It is worthwhile to note that the overall highest adsorption capacity was noted to be 10.6 mmol/g for CO 2 in immature II-D kerogen at 20 MPa and 323 K (Figure 1d). To visualize this better, a nanopore layer model of type II-D kerogen is shown (Figure 2), indicating the adsorption behavior of all gases, and a large cluster of CO 2 molecules is evident ( Figure 2). In addition, all kerogen structures depicted mainly type I adsorption behavior for gases, consistent with recent findings [52,69,70]. This observation is also in agreement with CO 2 and CH 4 adsorptions on coal [71]. In the case of H 2 adsorption, however, no attempt on kerogen is available to compare with the results of this study. Note, however, that here, the kerogen has a strong affinity for CO 2 , i.e.,~1.7 times than CH 4 and 4.5 times more than H 2 , which can be attributed to kerogen functional groups, which have a notable effect on the adsorption of CO 2 , CH 4 , and H 2 because of their remarkable adsorption energy for CO 2 over CH 4 and H 2 [69]. It can be noted that kerogens exhibited a small deviation from a type I adsorption behavior for H 2 gas. This particular behavior can be credited to the small molecular mass of H 2 (2.016 g/mole [6]) or low density, which promotes the weak intermolecular interaction of H 2 with organic matter and affects adsorption thermodynamics, and the associated bonding between adsorbate and adsorbent is a strong function of the density of a gas [47].
Hence, in short, the results advise a significant capability for gas disposal in underground organic-rich (kerogen) shale formations via adsorption trapping, especially for overmature kerogens. Furthermore, the observed adsorption isotherms are of great importance to be used as input in reservoir-scale assessment to investigate organic-rich porous media [71]. -a small increase in adsorption with a further increase in pressure until equilibrium is established. As a comparison, in the literature data from Zhao et al. [37] for similar kerogen (without nanopores), the two data points for II-A, II-C, and II-D (at 5 MPa and 323 K and 10 MPa and 323 K, plotted in Figure 1a,c,d) indicated a relatively lower adsorption capacity under similar conditions compared with our results. This underestimation could be attributed to the absence of nanopores with major control over the adsorption behavior, and thus the presence of nanopores (as in our models) suggests greater adsorption capacity.
It is worthwhile to note that the overall highest adsorption capacity was noted to be 10.6 mmol/g for CO2 in immature II-D kerogen at 20 MPa and 323 K (Figure 1d). To visualize this better, a nanopore layer model of type II-D kerogen is shown (Figure 2), indicating the adsorption behavior of all gases, and a large cluster of CO2 molecules is evident ( Figure 2). In addition, all kerogen structures depicted mainly type I adsorption behavior for gases, consistent with recent findings [52,69,70]. This observation is also in agreement with CO2 and CH4 adsorptions on coal [71]. In the case of H2 adsorption, however, no attempt on kerogen is available to compare with the results of this study. Note, however, that here, the kerogen has a strong affinity for CO2, i.e., ~1.7 times than CH4 and 4.5 times more than H2, which can be attributed to kerogen functional groups, which have a notable effect on the adsorption of CO2, CH4, and H2 because of their remarkable adsorption energy for CO2 over CH4 and H2 [69]. It can be noted that kerogens exhibited a small deviation from a type I adsorption behavior for H2 gas. This particular behavior can be credited to the small molecular mass of H2 (2.016 g/mole [6]) or low density, which promotes the weak intermolecular interaction of H2 with organic matter and affects adsorption thermodynamics, and the associated bonding between adsorbate and adsorbent is a strong function of the density of a gas [47]. Hence, in short, the results advise a significant capability for gas disposal in underground organic-rich (kerogen) shale formations via adsorption trapping, especially for overmature kerogens. Furthermore, the observed adsorption isotherms are of great importance to be used as input in reservoir-scale assessment to investigate organic-rich porous media [71].

Gases Adsorption Behavior Against Temperature
The adsorption behavior on four kerogen structures of the gases (CO2, CH4, and H2) was evaluated at 323 K, 373 K, and 423 K ( Figure 3). Clearly, adsorption decreased with increasing temperature for all kerogen structures. For example, at a fixed pressure of 20 MPa for II-A kerogen, the adsorbed amount of CO2, decreased from 8.8 mmol/g to 5.8 mmol/g (i.e., a 66% reduction) when the temperature of the system was elevated from 323 K to 423 K (Figure 3a), indicating a prominent decline. Similar trends were evident for CH4 and H2, i.e., a decline from 5.6 mmol/g to 3.7 mmol/g (↓66%) for CH4 and from 3.0 to 2.9 mmol/g (↓75%) for H2 for the same temperature increment (Figure 3a). At the same temperature range at a fixed pressure of 20 MPa, the adsorption capacity of the gases in other kerogens (II-B, II-C, and II-D) decreased with similar trends, as noted in II-D (Figure 3b-d and Table 1). Thus, the adsorption capacity is sensitive to temperature, and the lowtemperature shale gas reservoir demonstrated greater gas storage potential than the hightemperature shale formation. This phenomenon was also observed in shale adsorption tests [52,72,73].
The temperature directly caused the gas molecules to leave the adsorption site by high kinetic energy and escape to the bulk-free phase, i.e., a reduction in the adsorbed phase density with increasing temperature [26]. Consequently, the amount of adsorbed gas decreased with increasing temperature [73]. Moreover, the wetting behavior of shale could be another factor responsible for the lower adsorption of gases at higher temperatures. This is evident from the reduction in the water's advancing and receding contact angles with increasing temperature on shale surfaces [74] as well as coal samples [75], i.e., the samples showed less affinity toward CO2 at higher temperatures. However, further investigations are required to confirm these relationships. Thus, low-temperature shale appears to be most suitable for gas storage.

Gases Adsorption Behavior against Temperature
The adsorption behavior on four kerogen structures of the gases (CO 2 , CH 4 , and H 2 ) was evaluated at 323 K, 373 K, and 423 K ( Figure 3). Clearly, adsorption decreased with increasing temperature for all kerogen structures. For example, at a fixed pressure of 20 MPa for II-A kerogen, the adsorbed amount of CO 2 , decreased from 8.8 mmol/g to 5.8 mmol/g (i.e., a 66% reduction) when the temperature of the system was elevated from 323 K to 423 K (Figure 3a), indicating a prominent decline. Similar trends were evident for CH 4 and H 2 , i.e., a decline from 5.6 mmol/g to 3.7 mmol/g (↓66%) for CH 4 and from 3.0 to 2.9 mmol/g (↓75%) for H 2 for the same temperature increment (Figure 3a). At the same temperature range at a fixed pressure of 20 MPa, the adsorption capacity of the gases in other kerogens (II-B, II-C, and II-D) decreased with similar trends, as noted in II-D (Figure 3b-d and Table 1). Thus, the adsorption capacity is sensitive to temperature, and the low-temperature shale gas reservoir demonstrated greater gas storage potential than the high-temperature shale formation. This phenomenon was also observed in shale adsorption tests [52,72,73].

Gases' Adsorption Capacity Versus Thermal Maturity
The thermal maturity of a shale sample is known to influence its gas storage capacity. While vitrinite reflectance (Vr) is typically used as an indicator of thermal maturity [76],  The temperature directly caused the gas molecules to leave the adsorption site by high kinetic energy and escape to the bulk-free phase, i.e., a reduction in the adsorbed phase density with increasing temperature [26]. Consequently, the amount of adsorbed gas decreased with increasing temperature [73]. Moreover, the wetting behavior of shale could be another factor responsible for the lower adsorption of gases at higher temperatures. This is evident from the reduction in the water's advancing and receding contact angles with increasing temperature on shale surfaces [74] as well as coal samples [75], i.e., the samples showed less affinity toward CO 2 at higher temperatures. However, further investigations are required to confirm these relationships. Thus, low-temperature shale appears to be most suitable for gas storage.

Gases' Adsorption Capacity versus Thermal Maturity
The thermal maturity of a shale sample is known to influence its gas storage capacity. While vitrinite reflectance (Vr) is typically used as an indicator of thermal maturity [76], here, we used the elementary analysis of the four kerogen structures to establish the influence of maturity; this is because this study was based on kerogen models as opposed to a physical shale sample. The percentage of aromatic fixed carbon (obtained from NMR [77]) was lowest in II-A kerogen (40%) and highest in II-D kerogen (80%). Similarly, the XPS analysis demonstrated a similar trend [77]-the lowest aromatic carbon in II-A (40%) and the highest in II-D kerogen (72%)-consistent with overmature kerogen. Thus, on the basis of these model parameters, kerogen maturity was in the order of II-D > II-C > II-B > II-A. The adsorption capacity of the three gases demonstrated a clear increase with increasing kerogen maturity. This behavior can be attributed to specific functional groups, i.e., H, O, N, and S, and an increase in effective pore volume, as both are correlated with organic matter maturity, which is proportional to adsorption capacities [69,78,79]. Typically, at a particular pressure and temperature, the adsorption capacity followed the trend II-A < II-B <II-C < II-D, and the adsorption capacity increased with increasing carbon content (Figure 4). With an increase in carbon content from 40% to 80%, the adsorption capacity increased from 2.4 to 3.0 mmol/g for H 2 (Figure 4a), 7.7 to 9.5 mmol/g for CO 2 (Figure 4b), and 4.7 to 6.3 mmol/g for CH 4 (Figure 4c) at 15 MPa and 323 K. It is noteworthy to mention that the carbon content develops microporous characteristics in shale and contributes to the surface area and total pore volume. These factors can be attributed to a surge in absolute H 2 , CO 2 , and CH 4 adsorption above 50% of the carbon content (which can be referred to as the critical carbon content).
3, x FOR PEER REVIEW 8 of 18 here, we used the elementary analysis of the four kerogen structures to establish the influence of maturity; this is because this study was based on kerogen models as opposed to a physical shale sample. The percentage of aromatic fixed carbon (obtained from NMR [77]) was lowest in II-A kerogen (40%) and highest in II-D kerogen (80%). Similarly, the XPS analysis demonstrated a similar trend [77]-the lowest aromatic carbon in II-A (40%) and the highest in II-D kerogen (72%)-consistent with overmature kerogen. Thus, on the basis of these model parameters, kerogen maturity was in the order of II-D> II-C> II-B> II-A. The adsorption capacity of the three gases demonstrated a clear increase with increasing kerogen maturity. This behavior can be attributed to specific functional groups, i.e., H, O, N, and S, and an increase in effective pore volume, as both are correlated with organic matter maturity, which is proportional to adsorption capacities [69,78,79]. Typically, at a particular pressure and temperature, the adsorption capacity followed the trend II-A < II-B <II-C < II-D, and the adsorption capacity increased with increasing carbon content ( Figure 4). With an increase in carbon content from 40% to 80%, the adsorption capacity increased from 2.4 to 3.0 mmol/g for H2 (Figure 4a), 7.7 to 9.5 mmol/g for CO2 ( Figure  4b), and 4.7 to 6.3 mmol/g for CH4 (Figure 4c) at 15 MPa and 323 K. It is noteworthy to mention that the carbon content develops microporous characteristics in shale and contributes to the surface area and total pore volume. These factors can be attributed to a surge in absolute H2, CO2, and CH4 adsorption above 50% of the carbon content (which can be referred to as the critical carbon content).  Thus, it was confirmed that highly mature kerogen mainly adsorbs ably CO2 over CH4 and H2, while immature kerogen (II-A: carbon conten the lowest adsorption capacity. These results suggest a positive correla ogen maturity and the adsorption capacity of gases. These observatio  Thus, it was confirmed that highly mature kerogen mainly adsorbs more gas, preferably CO 2 over CH 4 and H 2, while immature kerogen (II-A: carbon content = 40%) showed the lowest adsorption capacity. These results suggest a positive correlation between kerogen maturity and the adsorption capacity of gases. These observations are consistent with previous findings on CO 2 and CH 4 adsorption onto shale surfaces [52,53,78]. A recent investigation by Arif et al. [26] also found a consistent increase in H 2 adsorption in coals with increasing carbon content [26].

Effect of Kerogen Porosity on Adsorption
The pore size distribution of the samples investigated here suggests that II-D exhibited the largest porosity (= 0.144), followed by II-C (= 0.075), II-B (= 0.073), and II-A (= 0.056), in descending order [80], i.e., the porosity increased with increasing thermal maturity from II-A to II-D kerogens. This observation is in agreement with a previous study [81]. Accordingly, with an increase of micropores, porosity was increased, and thus II-D offered the maximum adsorption capacity, and II-A kerogen offered the minimum. For example, at a fixed pressure (20 MPa) and temperature (373 K), the CO 2 adsorption capacity of type II-A kerogen was 7.3 mmol/g, while type II-D adsorbed 8.9 mmol/g under the same conditions ( Figure 1). Thus, a higher kerogen porosity promoted greater gas adsorption. Similar trends were evident for other gases (Figure 1).
Previous studies have evaluated the impact of pore size on gas adsorption potential in kerogen structures and shale and have noted that the adsorption capacity is indirectly correlated with the pore size increases [82][83][84][85][86]. The reason behind this could be limited adsorption heat and interaction energy with increased pore size [83]. This observation underpins the phenomenon of adsorption via enhanced specific surface area [86,87]. Notably, smaller micropores (<2 nm), evident in all kerogens, can provide a greater surface area and thus greater gas adsorption capacity [47]. However, the average pore sizes were almost the same in all kerogens.
Our results are in alignment with past studies [80,88,89], i.e., adsorption is sensitive to porosity. This can be attributed to the structural transformation, increased number of pores, and active sorption sites from immature to overmature shale that provide strong interaction sites to gases for adsorption. Small pore volumes were dominant in kerogens II-A and II-B, while large pore volumes contributed to kerogen II-C and II-D [78]. Thus, porosity's effect on the adsorption is clearly evident-a direct correlation was observed between kerogen porosity and adsorption capacity. Like the porosity effect, it is vital to extend this work to the effect of fracture permeability [90] on adsorption.

Kerogen Structure
We used four kerogen molecular models of varying maturity, i.e., immature (type II-A), top of oil window (type II-B), middle/end of oil window (type II-C), and postmature kerogen (type II-D) were considered ( Figure 5). These models are similar to those of Ungerer et al. [91], which were based on the analytical data corresponding to the work of Kelemen et al. [92]. The chemical compositions of the four kerogen models were C 252 H 294 O 24 N 6 S 3 , C 234 H 263 O 14 N 5 S 2 , C 242 H 219 O 13 N 5 S 2 , and C 175 H 102 O 9 N 4 S 2 . Note that such kerogen models exist in the organic-rich shale (e.g., Duvernay marine).
The chemical composition and physical properties of kerogen structures were in good agreement with the experimental data (e.g., X-ray and Nuclear Magnetic Resonance) [92], and the percentage of aromatic fixed carbon demonstrated a trend: the lowest aromatic carbon in II-A and highest in II-D kerogen. Thus, the kerogen maturity and porosity were in the order of II-D(overmature) > II-C(Middle and End Oil Window) > II-B(Top of Oil Window) > II-A(immature). The pores size distribution demonstrated that II-D contained the largest micropores, followed by II-C, II-B, and II-A in descending order.  [91], representative of real kerogen macromolecules before structural optimization. A single atomic unit of kerogen (also known as macromolecule) comprised of carbon (black), oxygen (red), sulfur (yellow), nitrogen (blue), and hydrogen (gray). Furthermore, immature kerogen had higher O/C and H/C ratios and lower aromaticity than the oil window and post-mature kerogens, while the key element of the structures was that the maturity increased as follows: II-A < II-B < II-C < II-D (see Table 2), which is plotted on Van Krevelen diagram illustrated in Figure 6. Specifically, II-D had the largest micropores, as evidenced by its high value of porosity compared with other considered kerogen types. Specifically, II-D had the largest micropores, as evidenced by its high value of porosity compared with other considered kerogen types.  [91], representative of real kerogen macromolecules before structural optimization. A single atomic unit of kerogen (also known as macromolecule) comprised of carbon (black), oxygen (red), sulfur (yellow), nitrogen (blue), and hydrogen (gray).
The chemical composition and physical properties of kerogen structures were in good agreement with the experimental data (e.g., X-ray and Nuclear Magnetic Resonance) [92], and the percentage of aromatic fixed carbon demonstrated a trend: the lowest aromatic carbon in II-A and highest in II-D kerogen. Thus, the kerogen maturity and porosity were in the order of II-D (overmature) > II-C (Middle and End Oil Window) > II-B (Top of Oil Window) > II-A (immature) . The pores size distribution demonstrated that II-D contained the largest micropores, followed by II-C, II-B, and II-A in descending order. Furthermore, immature kerogen had higher O/C and H/C ratios and lower aromaticity than the oil window and post-mature kerogens, while the key element of the structures was that the maturity increased as follows: II-A < II-B < II-C < II-D (see Table 2), which is plotted on Van Krevelen diagram illustrated in Figure 6. Specifically, II-D had the largest micropores, as evidenced by its high value of porosity compared with other considered kerogen types. Specifically, II-D had the largest micropores, as evidenced by its high value of porosity compared with other considered kerogen types.  Figure 6. Kerogen structure classification indicated as increasing order of maturity (modi [94]). White arrow shows increased level of maturity.

Kerogen Model Construction
A few previous MD simulation studies [52,58] have been carried out to dev condensed kerogen using a large-scale atomic/molecular massively parallel si (LAMMPS) [80]. Polymer-consistent forcefield plus (pcff++) was used in molec namics [93]; it describes atom dispersion/repulsion (Lennard-Jones potential 6molecular, and electrostatic interactions and has been recognized as a reliable fo for thermodynamic characteristics [77,95]. Kerogen structures of different maturities and types containing different un used. A pressure of 20.7 MPa and a temperature of 350 K were considered to prog simulation and were supposed to be representative of reservoir conditions. The M ulation considered initialization (9.5 cutoff value and periodic boundary) and ene imization (molecular positions and velocity proper configuration). Subsequently, (isochoric-isothermal) and NPT (isobaric-isothermal) simulations were run at 3 250 ps and 200 ps, respectively. Through three continuous NPT steps, the tem was gradually decreased from 350 K to 336 K to attain faster convergence of kerog as depicted by the final structure in Figure 7. To study the adsorption on the su kerogen, a nanopore was created in kerogen to expose the pore space to host the CO2, CH4, or H2), which led to adsorption on the surface. Unlike absorption, the a molecules do not penetrate the kerogen structure, and thus there was no chance of structural changes. Thus, the sum of adsorption and absorption, sorption, is equiv Figure 6. Kerogen structure classification indicated as increasing order of maturity (modified from [94]). White arrow shows increased level of maturity.

Kerogen Model Construction
A few previous MD simulation studies [52,58] have been carried out to develop the condensed kerogen using a large-scale atomic/molecular massively parallel simulator (LAMMPS) [80]. Polymer-consistent forcefield plus (pcff++) was used in molecular dynamics [93]; it describes atom dispersion/repulsion (Lennard-Jones potential 6-9), intermolecular, and electrostatic interactions and has been recognized as a reliable forcefield for thermodynamic characteristics [77,95].
Kerogen structures of different maturities and types containing different units were used. A pressure of 20.7 MPa and a temperature of 350 K were considered to progress the simulation and were supposed to be representative of reservoir conditions. The MD simulation considered initialization (9.5 cutoff value and periodic boundary) and energy minimization (molecular positions and velocity proper configuration). Subsequently, the NVT (isochoric-isothermal) and NPT (isobaric-isothermal) simulations were run at 336 K for 250 ps and 200 ps, respectively. Through three continuous NPT steps, the temperature was gradually decreased from 350 K to 336 K to attain faster convergence of kerogen units, as depicted by the final structure in Figure 7. To study the adsorption on the surface of kerogen, a nanopore was created in kerogen to expose the pore space to host the gas (i.e., CO 2 , CH 4 , or H 2 ), which led to adsorption on the surface. Unlike absorption, the adsorbed molecules do not penetrate the kerogen structure, and thus there was no chance of internal structural changes. Thus, the sum of adsorption and absorption, sorption, is equivalent to the total storage capacity. The kerogen model (e.g., II-D) used in this study is visualized in Figure 8; the other kerogen structure depicts a similar illustration of active space for adsorption.
where represents the charges, and are the separation distances from two force centers, is the relative permittivity, denotes the zero-interaction potential force distance, and is the highest amplitude.

Simulation Detail
The sorption was simulated by the Monte Carlo (MC) technique using the grandcanonical Monte Carlo (GCMC) approach [52,69,94] under a wide range of pressures (2.75 to 20 MPa) and temperatures (323 to 423 K). Moreover, ASPEN software was used with the Peng-Robinson equation of state to calculate fugacity coefficients of host molecules (i.e., H 2 , CH 4 , and CO 2 ) and converted into chemical potential in the GCMC simulation. Note that the host molecules were defined as united atoms. A molecular loading approach was further adopted to validate the molecular simulation, which showed an acceptable match between the empty cell yield density and the experimental NIST data for CO 2 , CH 4 , and H 2 (see Figure 9).

Conclusions
In this study, the adsorption capacities of H2, CO2, and CH4 were modeled on four kerogen structures of varying maturities under a wide range of pressures and temperatures. The adsorption capability of organic-rich matter (kerogen) improved with increasing pressure and decreased with temperature, regardless of kerogen maturity and gas type. The maximum adsorption was 10.6 mmol/g for CO2, 7.5 mmol/g for CH4, and 3.7 mmol/g for H2 in overmature II-D kerogen at 20 MPa and 323 K. Furthermore, the adsorption capacity was directly associated with thermal maturity, carbon content, and porosity at a certain pressure and temperature, i.e., II-D presented the highest adsorption, while all kerogens displayed mainly type I behavior for all gases. For all kerogens, adsorption followed the trend CO2 > CH4 > H2, attributed to the larger CO2 molecular size, which increased its affinity toward the kerogen. Furthermore, the available information from elementary analysis in terms of the pore size distribution was consistent with the adsorption trends. The porosity of kerogens and adsorption capacities of gases followed the order II-D > II-C > II-B > II-A, showing a direct correlation between adsorption capacity and kerogen porosity. Generally, overmature kerogen offered the maximum adsorption capacity at the maximum pressure and minimum temperature.
These findings, therefore, contribute to the preliminary datasets of organic-rich shale reservoirs in terms of kerogen adsorption affinity towards different gases and related logical intellection of adsorption mechanisms in kerogens. In summary, the findings suggest that mature shale formations with relatively high pressure and low temperature are highly suitable for gas storage. These results are also important to understand the potential of unconventional shale for the competitive potential of CO2 and H2 storage and thus contribute to strategies for carbon emission/hydrogen economy. In addition, this work can be extended in the presence of brine phase for its effect on adsorption. Interaction between kerogen and host molecules took place using the 6-9 LJ function (Equation (1)) with a grid spacing of 0.2 Å. For cross interactions, the Lorentz-Berthelot mixing rules (Equations (2) and (3)) were used. Upon the adsorption of gas molecules over kerogen up to a certain value, equilibrium was reached. The number of interactions was set at 0.35 million. At the end of the simulation, the total average adsorbed gas molecules were obtained as a function of chemical potential. Further explanation of the GCMC simulation procedure can be found in the literature [52,58].
where r ij represents the charges, q i and q j are the separation distances from two force centers, 0 is the relative permittivity, σ denotes the zero-interaction potential force distance, and is the highest amplitude.

Conclusions
In this study, the adsorption capacities of H 2 , CO 2 , and CH 4 were modeled on four kerogen structures of varying maturities under a wide range of pressures and temperatures. The adsorption capability of organic-rich matter (kerogen) improved with increasing pres-sure and decreased with temperature, regardless of kerogen maturity and gas type. The maximum adsorption was 10.6 mmol/g for CO 2 , 7.5 mmol/g for CH 4 , and 3.7 mmol/g for H 2 in overmature II-D kerogen at 20 MPa and 323 K. Furthermore, the adsorption capacity was directly associated with thermal maturity, carbon content, and porosity at a certain pressure and temperature, i.e., II-D presented the highest adsorption, while all kerogens displayed mainly type I behavior for all gases. For all kerogens, adsorption followed the trend CO 2 > CH 4 > H 2 , attributed to the larger CO 2 molecular size, which increased its affinity toward the kerogen. Furthermore, the available information from elementary analysis in terms of the pore size distribution was consistent with the adsorption trends. The porosity of kerogens and adsorption capacities of gases followed the order II-D > II-C > II-B > II-A, showing a direct correlation between adsorption capacity and kerogen porosity. Generally, overmature kerogen offered the maximum adsorption capacity at the maximum pressure and minimum temperature.
These findings, therefore, contribute to the preliminary datasets of organic-rich shale reservoirs in terms of kerogen adsorption affinity towards different gases and related logical intellection of adsorption mechanisms in kerogens. In summary, the findings suggest that mature shale formations with relatively high pressure and low temperature are highly suitable for gas storage. These results are also important to understand the potential of unconventional shale for the competitive potential of CO 2 and H 2 storage and thus contribute to strategies for carbon emission/hydrogen economy. In addition, this work can be extended in the presence of brine phase for its effect on adsorption.